For the other two people on the planet that have rescued HP, Dell, or other OEM motherboards from their stock cases, you might have noticed that the rear-panel audio jack on the motherboard stopped working. Apparently, some motherboards (an HP dC7100 CMT in my case) will turn off the rear-panel audio jack if the front-panel audio connector is disconnected. As it turns out, this is actually quite an easy fix.
According to Intel’s official front-panel connector specifications (see attached screenshot for a jumper layout), the motherboard uses pins 5, 6, 7,9 and 10 to detect whether or not the front-panel audio jack is connected to the system. To bypass the need for the front-panel connector, simply short pin 5 to pin 6 and pin 7 to pins 9 and 10 using some solder. After that, you should be solid.